Fig. 5
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Evolution of the explicit solution for Δt = 10−5 s (solid), compared to the first- order analytical approximation (dashed). Here, the solution for every 0.4 seconds until 3.2 seconds is shown with lines from dark to light. The relative error of the Gaussian profile quickly becomes comparable to that of the self-similar profile for solutions in the χt >> 1 regime.
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